Wednesday, November 18, 2015

This applies to other similar and earlier Casio calculators. Please
consult your manual if you have a different model. This refers to
Casio models that have textbook entry and output, such as the fx-115ES (Plus),
fx-991ES (Plus), fx-991EX Classwiz, and fx-570EX Classwiz.

Always Get an Approximate Answer
In the Math input mode, the Casio attempts to return an exact answer
(fractions, terms of π, terms of square roots). If you want to get an
approximate answer from the get go, all that is needed is to press [SHIFT], [ =
] (≈).

Using a Formula
Steps:

1. Enter your formula.
2. Press [CALC].
3. Enter a value for each variable prompted, then press [ = ].
4. For the Classwiz models: You can scroll up and down between variables.

Example:

(A^2 + B^2)^(1/3)

A = 3, B = 4, result 2.924017738
A = 5, B = 10, result 5

Solve f(X) = 0

Steps:

1.Enter f(X).On the Classwiz
series, you can use the [ x ] button.There is no need to enter the “=0”.

2.Press [SHIFT], [ CALC ] (SOLVE)

3.Enter a guess and press [ = ].

Example:

(Radians Mode)

X sin(X) – 1 with guess X = π, result:X = 2.772604708

Tip:I prefer to use X, but you should be able to use any of the other
variables available (A, B, C, D, E*, F*, Y, M).*E and F are available on later models.

For the fx-991EX Classwiz (I think
this applies to the fx-570EX Classwiz as well):Press [SHIFT] [ 8 ] (CONV).Select
a category and select a conversion.

For the fx-115ES PLUS and earlier
models (non-Classwiz models):Press
[SHIFT] [ 8 ] (CONV) and enter a code.For the fx-115ES PLUS, the conversions are listed both in the manual and
the hard slide on case.

Here is a sample of the conversions
offered on the fx-115ES PLUS:

01

in → cm

19

km/h → m/s

35

lbf/in^2 → kPa

02

cm → in

20

m/s → km/h

36

kPa → lb/in^2

07

mi → km

21

oz → g

37

°F → °C

08

km → mi

22

g → oz

38

°C → °F

23

lb → kg

24

kg → lb

3.Press [ = ].

Please be aware the older models may
not have the conversion function.

Factoring an Integer

‘1.Enter an integer then press [ = ].

‘2.Press [SHIFT], [ ° ‘ ‘’ ] (FACT)

Examples:

188 = 2^2 * 47

2506 = 2 * 7 * 179

Please be aware the older models may
not have the factoring function.

Calculus

Remember for derivative (d/dx),
integral ( ∫ ), sum ( Σ ), and product ( Π )*, the variable used is X.*Product may not be available on all
models.

Inverse and Determinant of a Matrix

For these calculators, matrices are a
separate mode.I assume that you know
how to edit and define matrices.

This is a sum that can’t be easily stated in summation
statement (Σ f(x)).

On the HP Prime, I programmed this as:

EXPORT TEST1112(n)

BEGIN

LOCAL k, t:=0;

FOR k FROM 1 TO n DO

t:=(t+1)^-1;

END;

RETURN t;

END;

The result seems to converge at 0.6180339785 when n ≥
27. Note that 0.6180339785 = ϕ – 1,
where ϕ is the Golden Ratio ( ϕ = (√5 + 1)/2)

Fibonacci Gets
Involved

Note that:

k =

t =

1

1

2

(1 + 1)^-1 = 1/2

3

(1 + 1/2)^-1 = (3/2)^-1 = 2/3

4

(1 + 2/3)^-1 = (5/3)^-1 = 3/5

5

(1 + 3/5)^-1 = (8/5)^-1 = 5/8

6

(1 + 5/8)^-1 = (13/8)^-1 = 8/13

7

(1 + 8/13)^-1 = (21/13)^-1 = 13/21

We get a sequence of terms {1, 1/2, 2/3, 3/5, 5/8, 8/13,
13/21, 21/34, 34/55, 55/89, 89/144, …} where each term takes the fraction a/b,
a is the kth Fibonacci number and b is the (k+1)th Fibonacci number. Can we show that this sequence of partial
sums is convergent?

Each partial sums of the series takes the form F_k / F_k+1
where F is the Fibonacci number.

3. When you finished
plotting the final corner point, press [ Enter ] one last time. This connects the last corner point with the
first corner point. Hence, it is like
go to the final point and press [ Enter ] twice.

With Parts 1 and 2, we will start with a clear plot screen,
with a Plot window of XRange = [ -16, 16 ], YRange = [ -11, 10.9 ], ticks are
at 1. This lesson will focus on drawing
line segments, parallel, and perpendicular lines.

Midpoint on a Line

For this part, put the line segment anywhere you wish.

1. Press (Cmds), 3
for Line, 1 for Segment. You are prompted
to select on the segment’s end points. Press
[ Enter ] to select the end point.

2. Select the other end of segment and press [ Enter ]. The segment is designated as object GC.

3. For the Midpoint,
press (Cmds), 2 for Point, 3 for Midpoint.
Select the line segment you have just drawn. Remember, when you cursor over objects that
you are about to select, that object turns red. Press [ Enter ]. The midpoint is plotted, as object GD.

Note that the coordinates the midpoint are not
displayed. Learn how to display the
coordinates in the next segment.

Display a Point’s
Coordinates

There are two ways to display a point’s coordinates. Try both methods and see which method works
better for you. You can use these
methods of displaying the coordinates for any point.

Either way, the coordinates of the point are displayed on
top of the screen.

For the next part of the lesson, please clear the plot
screen.

Draw Parallel and Perpendicular
Lines

1. Draw a line. To recall, press (Cmds), 3 for Line, 3 for
Line. Place the line anywhere you wish,
at any angle you wish. In the pictures
that are displayed, I just chose to place a horizontal line for demonstration purposes
(boring, huh?)

2. Parallel
Line: Press (Cmds), 3 for Line, 4 for
// (Parallel) . Select the line you drew
and press [ Enter ]. Place the parallel
line with a second [ Enter ]. A
parallel line is drawn.

Friday, November 6, 2015

Like Part 1, we’ll use a Plot window of XRange = [ -16, 16
], YRange = [ -11, 10.9 ], ticks are at 1.
For this lesson, we are going to focus on triangles. Start with a clear Plot Screen ([Shift], [
Esc ] (Clear)).

Drawing a Triangle

1. On the plot
screen, press the soft key (Cmds), then select 4 for Polygon and 1 for Triangle.

2. Select the first vertex
(corner point) and press [ Enter ]. For
this lesson, put the triangle wherever you want.

3. Place the second
and third vertex. Press [ Enter ] after
each point. The vertices are labeled A,
B, and C.

Finding an Angle

The steps will demonstrate how to find the angle. Be aware that the direction you enter the
vertexes will determine the sign of the angle.

1. Press (Cmds), 9
for Measure, 6 for Angle.

2. Select one vertex,
press [Enter]. Follow the triangle to
select the second vertex (where the angle will be measured), press [ Enter
]. Follow that with a third vertex and
press [Enter]. The angle displayed on
top of the screen.

Resizing the Triangle

Click on one of the points of the points. Then drag the point with the arrow pad. When satisfied, press [ Enter ].

For the last part, clear the screen.

Reflect a Triangle –
reflect about a point

1. Clear the screen. ([ Shift ] [ Esc ] (Clear))

2. Draw a triangle
with the vertices (-6, -4), (-6, 4), and (-12, 0).

3. Press (Cmds), 7
for Transform, 2 for Reflection.

4. You will be promoted
for a reflection point. For this exercise,
set the point at (0,0).